David Hope, the former archbishop of York, has resigned from his position as an honorary assistant bishop after a report into into allegations of abuse. Photograph: John Giles/PA

A former archbishop of York has resigned from his position as an honorary assistant bishop after a report into into allegations of child abuse by a former cathedral dean found “systemic failures” by the Church of England.

Last week’s report by Judge Sally Cahill QC said Lord Hope of Thornes failed to follow policy and take advice after he was informed of complaints against Robert Waddington relating to boys in Manchester and Australia.

The judge outlined failures by the C of E to respond properly to allegations of sex abuse against the late Robert Waddington, who was dean of Manchester between 1984 and 1993.

She said Lord Hope’s actions meant “opportunities were missed” to start an investigation which may have led to a prosecution before Waddington’s death seven years ago.

In a statement on Thursday, Lord Hope said: “After much prayerful and considered thought I wrote at the beginning of the week to the bishop of Leeds and in the light of the Cahill inquiry report I have submitted my resignation as honorary assistant bishop of Bradford, now West Yorkshire and the Dales, with immediate effect.

“This ends my nearly 50 years of formal ministry in the Church of England, which I have always sought to serve with dedication. I will certainly continue to pray for the important ongoing work with survivors.”

John Sentamu, the current archbishop of York, said he was saddened by Lord Hope’s decision.

Sentamu said: “I respect the prayerful decision made by my predecessor Lord David Hope. I am deeply saddened by his decision.

“He has served the Church of England with joyfulness, commitment, honesty and holiness. I personally thank him for his leadership as a priest, principal of a theological college, bishop and archbishop of the province of York; and above all as a dear brother in Christ.”

In her report last week, Judge Cahill said: “We consider the failings of Lord Hope were cumulative over the period, and arose as a result of Lord Hope not following the Church’s policies and instead dealing with a child protection issue in what appears to have been the way he would deal with a disciplinary matter or complaint.”

The judge said it is not possible to say what the consequences would have been if the former archbishop had acted differently.

But she said: “However, what is not speculative is, because of the actions he took, and his inaction on other occasions, opportunities were missed for an investigation which may have led to a prosecution during Robert Waddington’s lifetime.”

Lord Hope has always denied suggestions that he covered up allegations against Waddington, who died from cancer in 2007, but last week he offered a “personal and profound apology” to the victims if they felt they had been denied justice.

He said there was no recommendation at the time that allegations should be reported to the police.

“If all that has been learned by organisations and the public about child abuse in the last 15 years had been known in 1999 and 2004, I would certainly have acted differently,” he said.

Lord Hope added: “If either of the two persons concerned feel in the light of this report they have been denied the justice they deserve, then, on behalf of the Church of England, I offer my personal and profound apology.

“I genuinely believed that any complaints were being adequately dealt with by the respective dioceses in which they were alleged to have happened.”

The report detailed a range of allegations against Waddington that were first made to the C of E in 1999 but dated back as far as the 1950s.

Those who made allegations described abuse in Manchester, York, London, Carlisle and in Queensland, Australia.

Lord Hope stepped down as archbishop of York in 2005 when he returned to being a parish priest in Ilkley.